Please help me with this

Combine like terms 9-5=9x-6x

4vir4ik [10]

Answer:

4 = 3x

Step-by-step explanation:

9-5=9x-6x

Combine like terms

4 = 3x

We can solve for x

Divide by 3

4/3 = 3x/3

4/3 =x

7 0

4 years ago

A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

What is 3,333,333 rounded tp

Luba_88 [7]

To the nearest tenth: 3,333,330

To the nearest hundred: 3,333,300

To the nearest thousand: 3,333,000

To the nearest ten thousand: 3,330,000

To the nearest hundred thousand: 3,300,000

To the nearest million: 3,000,000

Hope that helps :)

5 0

3 years ago

Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x)/

elena55 [62]

Answer:

idkgu 6gv6tv6tv6tv6tv6vt6tv6tv6tv6tv6fv6tv6tv6tvguug uh

5 0

3 years ago

Which exponential function is represented by the values in the table?

astraxan [27]

ANSWER

The exponential function is
$f(x) = 3( {2}^{x} )$

EXPLANATION

Let the exponential function that is represented by the values in the table be of the form,

$f(x) = a( {b}^{x} )$

The points in the table must satisfy this exponential function.

We substitute the point,

$(0,3)$

to get,

$3 = a( {b}^{0} )$

This implies that,

$3 = a( 1 )$

$3 = a$

Our function now becomes,

$f(x) = 3( {b}^{x} )$

We gain, plug in another point yo find the value of b too.

Let us substitute
$(1,6)$

This implies that,

$6= 3( {b}^{1} )$

We divide through by 3 to obtain,

$2 = b$

Therefore the function is,

$f(x) = 3( {2}^{x} )$

The correct answer is A.

3 0

3 years ago

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